Abstract
Numbers in the Nth row of Pascal’s triangle represent binomial coefficients C(N, k), k = 0, 1, ..., N. I describe a relationship between the numbers in rows and in “diagonals” of Pascal’s triangle, provide an example and prove the formula. I show how this property appears useful for simplifying the Euler-Poisson equation for a class of optimization problems with constraints. A particular case of such optimization problems is finding geometric paths along which the maximally smooth trajectories have constant speed.
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